Mathematics Mock Test - 9 - CDS MCQ

We have a + c = e so possible summation 6+4=10 or 4+2 = 6.
Also b = 2d so possible values  4 = 2 * 2 or 10 = 5 * 2.
So considering both we have b = 10 , d = 5, a= 4 ,c = 2, e = 6.
Hence the correct option is B .

In this type of question, We need to find out the LCM of the given numbers.
LCM of 12, 15, 18 and 20:

⇒ 12 = 2 x 2 x 3
⇒ 15 = 3 x 5
⇒ 18 = 2 x 3 x 3
⇒ 20 = 2 x 2 x 5

∴ LCM = 2 x 2 x 3 x 5 x 3
Since the soldiers are in the form of a solid square. Hence, LCM must be a perfect square.
To make the LCM a perfect square, We have to multiply it by 5, hence, the required number of soldiers: 

= 2 x 2 x 3 x 3 x 5 x 5
= 900

Solve this question step by step:

1. Any number formed by this method is clearly divisible by 3.
2. Since it needs to be a square, it should be divisible by (3)^[2*k]. k varies over the natural numbers.
3. Now consider the original number. It has hundred 1’s, hundred 2’s and hundred 3’s. Sum of these digits is 600. This is not divisible by 9. Hence number is not divisible by 9.
4. If a number is divisible by (3)^[2*k], it is divisible by 3^k.
5. This number is not divisible by 3^k for any k > 1. 

Hence it is not a perfect square for any arrangement.

The ratio of number of male and female journalists in a newspaper office is 5:4.

The newspaper has two sections, political and sports.

If 30 percent of the male journalists and 40 percent of the female journalists are covering political news, what percentage of the journalists (approx.) in the newspaper is currently involved in sports reporting?

Let ‘9x’ be the number of total journalists in the office.
Then, we can say that the number of male and female journalists are ‘5x’ and ‘4x’ respectively.

It is given that 30 percent of the male journalists and 40 percent of the female journalists are covering political news. Hence, total number of journalists who are covering political news = 0.3*5x + 0.4*4x = 3.1x

Therefore, the total number journalists who are covering sports news = 9x – 3.1x = 5.9x.
Hence, the percentage of the journalists in the newspaper is currently involved in sports reporting = 5.9x/9x x 100 ≈ 

65 percent. Therefore, option B is the correct answer.

Assuming the income of Bimla = 100a, then the income of Amala will be 120a.

And the income of Kamala will be 120a*100/80=150a

If Kamala’s income goes down by 4%, then new income of Kamala = 150a-150a(4/100) = 150a-6a=144a

If Bimla’s income goes up by 10 percent, her new income will be 100a+100a(10/100)=110a

=> Hence the Kamala income will exceed Bimla income by (144a-110a)*100/110a=31

12.5 * 1.6 = 20 ; 20 + 12 – 20 = 12

Runs scored by Kohli in first 4 innings = 48*4 = 192
Average of 5 innings is 60, so total runs scored after 5 innings = 60*5 = 300
Hence runs scored by Kohli in fifth inning = 300 – 192 = 108
It is given that in 6th innings he scores 12 runs more than this, so he must score 120 in the sixth inning. Hence total runs scored in 6 innings = 300+120 = 420
Now average of last five innings is 78, so runs scored in last innings = 390
Hence runs scored in first inning = 420 – 390 = 30.

Mon + Tue + Wed = 35*3 = 105  ---------(1)
Tue + Wed + Thu = 30*3 = 90  -------------(2)
Thu = (1/2) Mon  ------------(3)

Eqn (1)-(2):
Mon-Thu = 15 ------------(4)

⇒ Mon - (1/2) Mon = 15
⇒ (1/2) Mon = 15
⇒ Mon =30
⇒ Thu = 30/2=15

Let x and y be mass of two alloys mixed.
In first alloy:

Gold = x × 1 / (1 + 2) = x/3
Silver = x × 2 / (1 + 2) = 2x/3

In second alloy:

Gold = y × 2 / (2 + 3) = 2y/5
Silver = y × 3 / (2 + 3) = 3y/5

In resulting alloy: 

Gold / Silver = 3 / 5
(x/3+2y/5) / (2x/3+3y/5) = 3 / 5
(x/3+2y/5) × 5 = (2x/3+3y/5) × 3
5x/3 + 2y = 2x + 9y/5
5x/3 - 2x = 9y/5 - 2y
-x/3 = -y/5
x / y = 3 / 5

Therefore, two alloys should be taken in ratio of 3 : 5.

Solve this question through options.
⇒  For instance, if he travelled at 25 km/h, his original speed would have been 24 km/h.
⇒ The time difference can be seen to be 6 minutes in this case = 60 / 24 – 60 / 25 = 0.1 hrs = 6 mins

Thus, 25 km/h is the correct answer. 

So Option A is correct

Time take for reaching B for ram is T = 5/5 = 1hr
Time taken for reaching B for Shyam is T = 5/10 = 1/2 hr

Its 10 am when ram reaches B and 10: 15 when Shyam reaches B , so they must meet each after 10 and before 10:15 for sure as ram starts back after reaching B

if we see for options 10: 10 am is the only answer

Any quadratic equation is of the form: x² - (sum of the roots)x + (product of the roots) = 0
where x is a real variable.

As the sum of the roots is 13 and the product of the roots is -140.
The quadratic equation with roots as 20 and -7 is: x² - 13x - 140 = 0.

Let three consecutive even natural numbers be 2x - 2, 2x and 2x + 2.

⇒ (2x - 2)² + (2x)² + (2x + 2)² = 1460
⇒ 4x² - 8x + 4 + 4x² + 8x + 4 = 1460
⇒ 12x² = 1452
⇒ x² = 121
⇒ x = ± 11
⇒ x = 11 [∵ The numbers are positive, i.e. 2x > 0 ⇒ x > 0]

Thus, Required numbers are 20, 22, 24.

We have, p² + 5 < 5p + 14

=> p² – 5p – 9 < 0

=> p<6.4 or p>-1.4
Hence, p ≤ 6, p > −1 will satisfy the inequalities

Let the roots of the equation x² + (a + 3) x- (a + 5) = 0 be equal to p, q

Hence, p + q = -(a + 3) and p x q = -(a + 5)

Therefore, p² + q² = a² + 6a + 9 + 2a +10 = a² + 8a + 19 = (a+4)² + 3

As (a + 4)2 is always non negative, the least value of the sum of squares is 3

Adding the two equations, tanØ = (m + n) / 2
Subtracting the two equations, sinØ = (m - n) / 2

Since, there are no available direct formula for relation between sinØ tanØ.
But we know that: cosec²Ø - cot²Ø = 1

If we look at the above image, A is the previous position of the boat. The angle of elevation from this point to the top of the lighthouse is 30 degrees.

After sailing for 50 m, Anil reaches point D from where the angle of elevation is 45 degrees. C is the top of the lighthouse.

Let BD = x

Now, we know tan 30 degrees = 1/ √3 = BC/AB

Tan 45 degrees = 1

=> BC = BD = x

Thus, 1/ √3 = BC/AB = BC / (AD+DB) = x / (50 + x)

Thus x (√3 -1) = 50 or x= 25(√3 +1) m

The answer is Option D.

Let the numbers 13a and 13b.

Then, 13a x 13b = 2028

⇒ ab = 12.

Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1
Now, the co-primes with product 12 are (1, 12) and (3, 4).

⇒ The required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).

N = greatest number that will divide 105, 4665 and 6905 leaving the same remainder in each case

⇒ N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
⇒ N = H.C.F. of 3360, 2240 and 5600 = 1120
Sum of digits in N = (1 + 1 + 2 + 0) = 4

CP = 20000
Profit = 25/100 of 20000 = 5000
SP = Profit + CP = 25000

New transaction

CP= 25000
Loss = 25% of 25000 = 6250
SP = CP - Loss = 18750

P's gain = 1250
TOTAL gain = 6250
Total gain % = 6250/20000 × 100 = 625/20 = 31.25%

So option C is correct

The total discount offered by E = 5% on 1,00,000 + 12.5% on 80,000 = 5,000 + 10,000 = 15,000.

If R wants to be as competitive, he should also offer a discount of Rs. 15,000 on 1,80,000.

Discount percentage = (15000/180000) x 100= 8.33% discount.

So option B is correct

Given, SI = Rs 929.20
P = ?
T = 5 years
R = 8%
P = (100 x SI) / RT
⇒ (100 x 929.20) / (8 x 5)
⇒ Rs. 2323

We need to know the S.I, principal and time to find the rate. Since the principal is not given, so data is inadequate.

• Total number of cards, n(S) = 52
• Total number of face cards, n(E) = 12 (4 Jacks, 4 Queens, 4 Kings)

Total number of balls = 2 + 3 + 2 = 7

► Let S be the sample space.

• n(S) = Total number of ways of drawing 2 balls out of 7 = ⁷C₂

► Let E = Event of drawing 2 balls, none of them is blue.

• n(E) = Number of ways of drawing 2 balls from the total 5 (= 7-2) balls = ⁵C₂
  (∵ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)

Given, log 27 = 1.431
⇒ log (3³) = 1.431
⇒ 3 log 3 = 1.431
⇒ log 3 = 0.477
∴ log 9 = log (3²) = 2 log 3
⇒ (2 x 0.477) = 0.954

log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + 1

⇒ log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + log₁₀ 10

⇒ log₁₀ [5 (5x + 1)] = log₁₀ [10(x + 5)]

⇒ 5(5x + 1) = 10(x + 5)

⇒ 5x + 1 = 2x + 10

⇒ 3x = 9

⇒ x = 3.

Explanation:

Let the price of each note book be Rs.x.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
=> y = 300/x 
(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy
=>5(300/x) - 10x - 50 = 0 => -150 + x² + 5x = 0
multiplying both sides by -1/10x
=> x² + 15x - 10x - 150 = 0
=> x(x + 15) - 10(x + 15) = 0
=> x = 10 or -15
As x>0, x = 10.

Explanation:

I. (a - 4)(a + 2) = 0
=> a = 4, -2
II. b² = 9
=> b = ± 3
-2 < 3, -2 > -3, 4 > 3, 4 > -3,
No relation can be established between a and b.